576 MAGNETIC FIELD. 



given directly by experiment. Finally, the ratio is sensibly 



cos 8' sin (0-5) 



equal to -- - when the displacements are very small, even when 



the angle is not strictly 90. 



1148. We may even eliminate the angles 6 and 6' by observation 

 of oscillations ; for when the needle is acted on by the field H + F, 

 and is displaced through the angle e, the couple Q which tends to 

 bring it back is, from equations (8) and (9), 



sin <o sin 6 . 



Q = C . ,a jr Sin c = FM - - Sin e, 

 sm (0 - 8) sin 8 



and the corresponding number N of oscillations, satisfies the equation 



. 



sm (0 - 8) sin 8 



An analogous expression for the number N' of oscillations relative 

 to the field H + F' gives 



F _ N 2 sin 8 

 '" 



and this equation now only contains the angles 8 and 8'. 



Comparing these equations (10) and (n), it follows, as a con- 

 dition to be verified by experiment, 



N 8 _sin(0-8') 



1149. USE OF GALVANOMETERS. The action of a magnetic 

 field may be compared with that of a current by very varied 

 experiments. 



Suppose, for instance, that a galvanometer, whose constant is G, 

 is placed in a field F, parallel to the frame, and that a current I, 

 determined in absolute value by some other instrument, is passed 

 through it, the deflection 8 of the needle will give the field F by 

 the equation 



Gl = FtanS. 



